MasterCard said earlier this year that it plans a new fee for digital wallet operators starting in June.

PayPal is not an official payment network in its own right. Instead, when people use PayPal to pay for something, the purchases are funded from their bank account or their credit and debit cards. Because of this, PayPal already pays huge amounts of fees to Visa, MasterCard and American Express whenever a PayPal purchase is funded with a credit card bearing those logos.

Shares of eBay Inc, owner of PayPal, the largest digital wallet operator, have been hit hard on concerns other payment networks may roll out similar fees, cutting into PayPal's profitability.

"I think it is totally appropriate to do that," Scharf said during the Barclays Emerging Payments Forum on Wednesday, when asked if Visa was planning a digital wallet fee.

Digital wallets are electronic versions of real wallets that store card and bank information and can be used to buy things online quickly and anonymously. These digital wallets are increasingly moving into the physical world, through consumers' use of smartphones while shopping in retail stores.

PayPal is moving from its online roots into the physical retailer world, where the vast majority of payments still take place. It is a big opportunity for the business, and that has driven eBay shares higher in the past year.

However, as a payment option in lots of physical stores, PayPal will be a bigger threat to networks like MasterCard, Visa and American Express, analysts say.

"Some of the people we compete with started out as one thing and they morph into another thing, and doing things online is very different than doing things at point of sale," Scharf said on Wednesday.

"We are always thinking about those relationships and they have changed," he added. "And if they changed enough that we think it warrants us to change something with us, we will do that."

A Visa spokesman declined to comment on Wednesday.

The MasterCard fee will be charged on "staged" digital wallets, such as PayPal, Google's Wallet, Square, iZettle in Europe and Intuit Inc's GoPayment, according to analysts.

Staged digital wallets typically share less information with card issuers and the networks, creating customer service problems and making it more difficult to deal with card rewards programs, analysts say.

"Allowing data to be passed through to our issuers and then not allowing data to be passed through to our issuers makes us re-think about our pricing and our rules," Scharf said on Wednesday.

Gil Luria, an analyst at Wedbush Securities, said it is "inevitable" that Visa will follow MasterCard's move and introduce a digital wallet fee of its own.

"This is a fully functioning duopoly. When one does something, the other one follows suit," Luria explained. "It was MasterCard's turn to exercise its market power. If they are allowed to do it then Visa will follow."